Nodal Point

The Nodal Point

		Determining the location of the Nodal Point (entrance pupil)

		The conventional approach

		A simple method

		Using a Laser Pointer

		Some examples using the Laser Pointer method

		Sigma 8mm

		Nikon 10.5mm

		Samyang 8mm

		Connections to other Pages

The Nodal Point of the lens (or more correctly, the entrance pupil) can be considered as the point at which the rays entering the lens converge. It can also be considered as the centre of perspective of the lens or the apparent pupil. This point can be considered as the Front Nodal Point as the lens also has a Rear Nodal Point and in a simple lens the two nodes converge to a single point.

The term Nodal Point is used here because for decades it has been accepted as the term defining the point where the rays entering the lens apparently converge and has been referred to by this nomenclature in a considerable number of Photogrammetric papers and publications, but let us not let terminology detract from the message. What we are interested in is the directions (or vectors) of the rays entering the lens.

It is important to know the location of this point (entrance pupil) for Photogrammetric purposes. To enable the correct origin and orientation in space of the rays used to compute the intersection when using the technique of Photographic Intersection it is important that this point is determined as accurately as possible. It is also vital that this point is known for applications such as using the photographic image on conjunction with HDS (High Definition Surveying) data and for any application for where an equirectangular image is to be produced using software such as PTGui.

Wild P32 Photogrammetric Camera Sigma 8mm f/3.5 EX DG Lens This point is also the ideal point to rotate your lens around when taking images to 'stitch' together to produce panoramic images. If you are creating a panorama of objects very close to the camera, or full 360° panoramas with a fisheye lens, then serious consideration needs to be given to this point, but if your panoramas are of features hundreds of metres from the camera, such a landscape panorama, then you will not need to give any thought to this point.

Photogrammetric camera lenses are constructed so as to be 'symmetrical'. The mounting of the Wild P32, shown in the image, on a theodolite was arranged so that the front nodal point of the lens was coincident with the standing axis of the theodolite when the telescope was truly horizontal even though this meant that the camera was not well balanced. In normal photographic lenses, such as those we would select for Photographic Intersection, this point is often not a single point but 'slides' along the principal ray of the lens depending on the angle between the ray being considered and the principal ray. For the purposes of Photographic Intersection the position of these points should be determined for the widest angle of view for the lens, although there is the opportunity to introduce the different locations as another parameter in the computation process.

Determining the location of the Nodal Point (entrance pupil)

The Nodal Point or entrance pupil can be measured as part of the camera and lens calibration process using a calibration rig constructed for determining the parameters of the camera and lens for photogrammetric purposes. Such setups are few and far between, and even if you do locate one, the cost of the calibration will probably be more than the value of the equipment you are calibrating, which defeats the object of using Photographic Intersection as a low cost method of accurately measuring 3D points. It is therefore desirable to find a way of determining the Nodal Point yourself with easy to obtain and low cost items.

The conventional approach ...

At the end of the 1970s, beginning of the 1980s, I used a method similar to that described by Michel Thoby with nails and banknotes except that I used needles and the face of an "E" survey staff or tape measure.


	The important thing is that the foreground objects do not obscure too much of the background and that the background has sufficient detail to identify accurately the part obscured in the image by the foreground objects.

The technique is to make an image of the scene, then use the detail of the background object obscured by the foreground objects to reconstruct the rays that converge at the Nodal Point and thus define it. It is imperative that nothing in the arrangement must be disturbed whilst a suitable print of the scene is made so that the rays can be accurately drawn. In the digital age this is not so much of a problem but when film is used keeping the scene intact can be a problem. A disadvantage of this method is that using nails or needles with a background quite near to the lens is that the lens is close focused to keep the detail sharp in the image, but that the lens will more likely to be focused at or near infinity when actually used for measurement. The Nodal Point can change with focusing in some lenses. This can be overcome by going outside and using canes, ranging rods or dowels as the foreground objects with say a building facade as the background image and with the camera and lens on a "Plane Table". Keeping the arrangement undisturbed whilst processing film and printing a decent size image was even more of a challenge! Note that the camera has been rotated around its principal ray so that the diagonal of the field of view is used to get the maximum angle of view, a technique that can be used with both the other methods following.

A simple method ...

A simpler method of determining the Nodal Point is to place an object (thin pole or wire) near the lens and align it with a more distant object. If the camera is rotated about the Front Nodal Point the two objects will be aligned when they are in the centre of the image and also when at each side of the image. If the objects are aligned when in the centre of the image but appear to separate as the camera is rotated then the rotation is not about the Nodal Point. This method may be simpler than the first method described, but is more fiddly and less accurate.

To determine the Front Nodal Point of a Nikon 18-70 mm zoom lens set at 18 mm, a 10 mm dowel was positioned some 7 m in front of the camera so that it was aligned with the apex of the roof of a house some 200 m away. The camera was rotated around the tripod mounting point in the base, which is behind the Nodal Point, and a point a similar distance in front of the Nodal Point to illustrate the apparent movement of the dowel relative to the roof apex if the camera is not rotated about the Front Nodal Point.

When the camera is rotated about the Front Nodal Point the dowel is still aligned with the apex of the roof of the house at both the Left and Right edges of the image. Note that this is at the Front Nodal Point for that particular angle of incidence if the lens does not have a single point for the Nodal Point as in some of the examples following.

In this case the camera was rotated about the tripod mounting point, which is behind the Nodal Point. This is the normal case for a camera mounted on a tripod using the ¼" Whitworth thread in the camera's base plate.

The dowel appears to the left of the apex of the roof at the left hand edge of the image and to the right of the apex of the roof at the right hand edge of the image.

To show the effect of the rotation of the camera in front of the Nodal Point the camera was mounted on a bar so that the rotation point was approximately as far in front of the Nodal Point as the ¼" Whitworth thread in the camera's base plate is behind the Nodal Point.

The dowel appears to the right of the apex of the roof at the left hand edge of the image and to the left of the apex of the roof at the right hand edge of the image.

Using a Laser Pointer ...

Determining the location of the Nodal Point of a Lens The most innovative and inspired method I have come across recently is that used by Michel Thoby with a laser pointer. As Michel states, you only need the lens for this method. However, having the lens mounted on a film camera with the shutter open on bulb and the back open means that you can calibrate any lens as the lens axis will always be the same height above the surface. This means that it is easier to construct your laser alidade with a fixed height for the laser above the surface. When the laser beam travels along the path of a ray that meets the Nodal Point, a very bright spot is seen on the surface (white card) placed behind the lens and the ray can be drawn on the paper. These rays can be constructed for a variety of angles of incidence and the Nodal Point determined.

This method is remarkably precise and accurate results can be obtained quickly and easily. The position of the lens, especially the front which will be used as the reference, can be orthographically projected onto the paper using a simple set square.

Determining the Nodal Point of a Lens using a Laser

Results from using the Laser Pointer method to determine the location of the Nodal Point

The position of the Nodal Point, and its behaviour, clearly depends on the lens design and construction.

	The Sigma 10 to 20mm f4-5.6 EX DC HSM Lens zoom lens actually has the Front Nodal Point at a point and this location remains the same irrespective of the distance the lens is focused for. It is the same point whether the lens is focuses at infinity or close focused. With the lens set at the 10mm end of the zoom, the Nodal Point is some 16mm back from the front of the lens and 6 mm behind the gold ring.

	The Front Nodal Point on the Sigma 10 to 20mm f4-5.6 EX DC HSM Lens zoom lens moves away from the front of the lens as the focal length is increased by zooming and is some 19mm back from the front of the lens when set at the 20mm focal length. At the 20mm setting the Nodal Point is coincident with the gold ring and remains in the same place as the lens is focused.

	The Nikon 28mm f2.8 D AF lens demonstrates how the Front Nodal Point "slides" along the principle ray (lens axis) in some lens designs. As the angle of view increases, the Nodal Point moves back, away from the front of the lens. Here the lens is focused at infinity and the Nodal Point is some 20mm from the front of the lens and shows a spread of some 4mm with the angles of view used.

	The Nikon 18 to 200mm f3.5-5.6 G AF-S VR lens set at 18mm shows a similar consistency to the Sigma 10 to 20mm, with a slight change between focus at infinity and close focused. For use with a Panoramic head for 360° Panoramas, the Nodal Point can be considered as 32mm back from the front rim of the lens.

	The Nikon 10.5mm f2.8 G ED Fisheye shows the reverse effect to the Nikon 28mm lens in that the Front Nodal Point "slides" along the principal ray but moves closer to the front of the lens as the angle of view increases. The Nodal Point for this lens also varies according to the focus and has less of a spread when close focused than when focused at infinity.

	The Sigma 8mm f3.5 EX DG Fisheye shows the same characteristics as the Nikon 10.5mm Fisheye lens in that the Front Nodal Point "slides" along the principal ray and moves closer to the front of the lens as the angle of view increases. The Nodal Point for this lens also varies according to the focus and has less of a spread when close focused than when focused at infinity.

	The Sigma 4.5mm f2.8 EX DC Fisheye shows the same characteristics as the Sigma 8mm Fisheye lens in that the Front Nodal Point "slides" along the principal ray and moves closer to the front of the lens as the angle of view increases.

	The Samyang 8mm f3.5 FISH-EYE CD shows the same pattern as the other fisheye lenses, but with a much tighter range for the entrance pupil, which is due to the different design as described by LensTip.com and Michel Thoby. This design would suggest that this is a more suitable lens for Spherical (360°) Panoramas than the "conventional" fisheye lenses and its considerably lower cost makes it an attractive option.




		Links to Panorama Related Sites and Software Links include PanoramaStudio, PTGui, Pano2VR, panoramic tripod head suppliers and 360° panoramas

		www.360hugh.co.uk Visit Hugh’s world of panoramas … A site that is being developed to relate specifically to panoramic photography to show the potential of this media and how it is able to convey much more than words or single images. If a picture is worth a thousand words then a panorama must be worth ten thousand, especially a 360° (or spherical) panorama where you can look all around and in any direction you wish to.

		Taking Panoramas If a picture is worth a thousand words then a panorama must be worth ten thousand, especially a 360° panorama where you can look all around, but how are they created?

		Making use of the Nodal Point of a Lens Comments on making use of the knowledge of the behaviour and location of the Nodal point of a lens for various Panorama and Photographic Intersection applications.

		The Nodal Point The case for the Nodal Point and usage of the term..

		Focus and Exposure Comments on getting the correct Focus and Exposure for making Panoramas.

		Lens Angle of View The Angle of View of a lens, or what the lens "sees", is useful for calculating the number of shots and their orientation for 360° panoramic photography.

		Spherical Panoramas with a Normal Lens Using a normal (rectilinear) lens for Spherical (360°) Panoramas.

		An Investigation into the use of different Lenses for 360° Panoramas A comparison of fisheye and rectilinear lenses for producing 360° Panoramas and importing the Cube Images into Leica Cyclone.

		Create your own Panoramas Panoramas are straightforward to create from images from just about any camera, with the help of low cost software. This page is intended to encourage you to create your own Panoramas.